whats the value of x if log((2x-2)to the base 3 + 7) to the base 2 = 2+log ((x-1)to the base 3 + 1) to the base 2

Question

its a question from logorithm

Answer 1

It is unclear what it is to the base 2.

 

 

But it looks like you have:

 

 log_3(2x - 2) + C = 2 + log_3(x-1) + k where C and k are some fixed number constants

                                  ''

 

Moving the log_3 on the right to the left side and the constants to the right side

 

log_3(2x-2) - log_3(x-1) = 2 + _K  where _K is just a fixed number constant involving k - C + 2

 

By property of Logs,   log (A/B) = log(A) - log(B)

 

so the left side is just

 

log_3(  (2x-2)/(x-1) ) = 2 + _K

 

log_3( 2(x-1)/(x-1)) = 2 + _K  <--- 2 factors out of the numerator in the argument of the log

 

log_3(2) = 2 + _K  <--- x-1 cancels out

 

log_3(2) - 2 + (k - C + 2)  

 

You can now plug in your number given for the constants

and solve for the undetermined coefficient

 

I've tried to point you in the right direction

Please repost the problem EXACTLY like it reads on the paper.